There are many instances where it would be desirable to inexpensively divide units of time or units of distance into smaller units. For example, in a range detector, the time elapsed between the outgoing signal and the incoming signal may be very short, on the order of nanoseconds, and the use of a standard reference clock to count the time elapsed would yield an inaccurate count resulting in inaccurate distance calculations.
In another example, in laser printers, it is often desirable to provide a transition from white-to-black (or vice versa) at various distances within a given line cell for high resolution. See U.S. Pat. No. 5,109,283 incorporated herein by this reference. A white-to-black or black-to-white signal, however, clocked at the printer's pixel clock rate of 10 MHz, is not resolved finely enough at the printer's laser diode to accurately phase transitions within a given cell (print pixel). Faster clocks are too expensive and/or not available to reference the black-to-white or white-to-black transitions at the resolution of one nanosecond corresponding to print cell distances on the order of microns required for high resolution graphic images.